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arXiv:1109.6753 · Physical Review B

Effects of external driving on the coherence time of a Josephson junction qubit in a bath of two-level fluctuators

Håkon Brox, Joakim Bergli, Y. M. Galperin

Published Dec 12, 2011• 8 citations
arXivHTMLPDF

Abstract

We study the effect of external driving on the two-level systems (TLSs) assumed to be a major obstacle in increasing the coherence time of solid-state Josephson junction qubits. We find, by use of a Bloch-Redfield approach, that external driving has two major effects on the TLS. The first is increased fluctuations between the two states of the TLS; the significance of this effect compared to thermal fluctuations depends on the energy splitting of the TLS compared to temperature. The second effect is a reduction in the intensity of the noise spectrum at low frequencies, and at the same time an increase in intensity around the renormalized Rabi frequency of the TLS and the driving frequency and at beatings between these two frequencies. Finally, we study the ensemble-averaged noise spectrum for a typical distribution of TLSs known to give origin to $1/f$ noise. We find that strong driving leads to reduced noise at low frequencies, and therefore to an increased dephasing time ${T}_{2}^{Q}$ of the qubit. However, this effect is exponentially suppressed when the driving frequency is large compared to temperature, as we typically find for Josephson qubits. We suggest that external driving at frequencies much lower than the qubit frequency might be used in order to enhance the the qubit coherence time.

DOI
10.1103/physrevb.84.245416

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We study the effect of external driving on the two-level systems (TLSs) assumed to be a major obstacle in increasing the coherence time of solid-state Josephson junction qubits. We find, by use of a Bloch-Redfield approach, that external driving has two major effects on the TLS. The first is increased fluctuations between the two states of the TLS; the significance of this effect compared to thermal fluctuations depends on the energy splitting of the TLS compared to temperature. The second effect is a reduction in the intensity of the noise spectrum at low frequencies, and at the same time an increase in intensity around the renormalized Rabi frequency of the TLS and the driving frequency and at beatings between these two frequencies. Finally, we study the ensemble-averaged noise spectrum for a typical distribution of TLSs known to give origin to 1/f1/f1/f noise. We find that strong driving leads to reduced noise at low frequencies, and therefore to an increased dephasing time T2Q{T}_{2}^{Q}T2Q​ of the qubit. However, this effect is exponentially suppressed when the driving frequency is large compared to temperature, as we typically find for Josephson qubits. We suggest that external driving at frequencies much lower than the qubit frequency might be used in order to enhance the the qubit coherence time.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and 1∕f1∕f1∕f noise in the Josephson junction critical current I0{I}_{0}I0​. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.
Two-level systems (TLSs) are the major source of dephasing of spin qubits in numerous quantum computing platforms. In spite of much effort, it has been difficult to substantially mitigate the effects of this noise or, in many cases, to fully understand its physical origin. We propose a method to make progress on both of these issues. When an oscillating field is applied to a TLS, stochastic resonance can occur and the noise spectrum is moved to higher frequencies. This shift in the TLS noise spectrum will increase the dephasing times of the qubits that they influence. Furthermore, the details of this effect depend on the physical properties of the noise sources. Thus one can use qubit spectroscopy to investigate their physical properties, specifically the extent to which the TLSs themselves possess quantum coherence. We find that it should be possible to determine the dephasing rate and the energy-level separation of the TLS themselves in this way.
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We consider two representative problems that deal with the fluctuator-induced decoherence from two very different perspectives-microscopic and macroscopic. In the first part, we consider an individual two-level system inside a Josephson junction shunted by a resistor. If the TLS modulates the Josephson energy and/or is optically active, it can be Rabi driven by the Josephson oscillation. The Rabi oscillations, in turn, translate into oscillations of current and voltage which can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS's contribution to the decoherence when the junction is used as a qubit. In the second part, we study the contribution of an ensemble of non-stationary glassy charge fluctuators on qubit decoherence. Low-temperature dynamics of insulating glasses is dominated by a macroscopic concentration of tunneling two-level systems. Due to exponentially broad distribution of their tunneling rates and the finite experimental manipulation timescales, some of the fluctuators are temporarily stuck in high-energy non-thermal states. We find that at low enough temperatures, non-stationary contribution due to these slow non-thermal fluctuators can dominate the stationary (thermal) one, and discuss how this effect can be minimized.
We study the charge noise SQ{S}_{Q}SQ​ in Josephson qubits produced by fluctuating two-level systems (TLSs) with electric-dipole moments in the substrate. The TLSs are driven by an alternating electric field of angular frequency $\ensuremath{\Omega}$ and electric field intensity III. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if I⪢IcI⪢{I}_{c}I⪢Ic​, where Ic{I}_{c}Ic​ is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density-matrix elements. To determine the dependence of the density-matrix elements on the ratio I/IcI/{I}_{c}I/Ic​, we find the steady-state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency fff and the ratio I/IcI/{I}_{c}I/Ic​. We find 1/f1/f1/f charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.